A differential linear matrix inequality (DLMI) approach is introduced for the solution of various linear continuous-time control problems. The proposed method permits the application of linear matrix inequalities (LMIs) to the solution of control design problems under uncertainty. These problems are solved for finite horizon linear systems while considerably reducing the overdesign inherent in previous methods. The new approach also allows for the solution of the output-feedback control problem for systems belonging to a finite set of uncertain plants with hardly any overdesign. Four examples are given to demonstrate the applicability of the new method.